My take from years of visiting this hotel is anything that has a door would be a suite. A junior suite would be a larger room but in the past we have received junior suites as stated by hotel that are more like a traditional suite with a door. These are usually in the older "renovated" area of the hotel without much of a higher view.
I think your timing is pretty good as can not think of any major Japanese holidays during the period. It is a weekend so that ALWAYS comes into play as a negative. Even with our multiple multiple stays I do not hold out hope anymore for exec suite. You should contact the hotel letting them know you are putting in for suite upgrade and also kindly asking for additional consideration if possible. We very much enjoyed our last upgrade and it was not a full suite. Enjoy Kyoto!